Intrinsic Transverse Motion of the Pion's Valence Quarks

Starting with the solution to the Bethe-Salpeter equation for the pion, in a beyond rainbow-ladder truncation to QCD's Dyson-Schwinger equations, we determine the pion's l_z=0 and |l_z|=1 leading Fock-state light-front wave functions (LFWFs) [labeled by ψ_{l z}(x ,k_T²)]. The leading-twist time-reversal even transverse momentum dependent parton distribution function (TMD) of the pion is then directly obtained using these LFWFs. A key characteristic of the LFWFs, which is driven by dynamical chiral symmetry breaking, is that at typical hadronic scales they are broad functions in the light-cone momentum fraction x . The LFWFs have a nontrivial (x ,k_T²) dependence and in general do not factorize into separate functions of each variable. For k_T²≲1 GeV² the k_T² dependence of the LFWFs is well described by a Gaussian; however for k_T²≳10 GeV² these LFWFs behave as ψ₀∝x (1 -x )/k_T² and ψ₁∝x (1 -x )/k_T⁴, and therefore exhibit the power-law behavior predicted by perturbative QCD. The pion's TMD naturally inherits many features from the LFWFs. The TMD evolution of our result is studied using both the b^* and ζ prescriptions which allows a qualitative comparison with Drell-Yan data.